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Kaon to two-pion decay and pion-pion scattering from lattice QCD

Wang, Tianle

In this work, we present a lattice QCD calculation of two closely related quantities: 1). The πœ‹πœ‹ scattering phase shift for both 𝑰=0 and 𝑰=2 channels at seven energies in total, and 2). The πœŸπ‘°=1/2, 𝛫 β†’ πœ‹πœ‹ decay amplitude 𝐴₀ and πœ–β€², the measure of direct CP violation. These two results improve our earlier calculation presented in 2015 [1]. The calculation is performed on an ensemble of 32Β³ Γ— 64 lattice with 𝛼⁻¹=1.3784(68)GeV. This is a physical calculation, where the chiral symmetry breaking is controlled by the 2+1 flavor MΓΆbius Domain Wall Fermion, and we take the physical value for both kaon and pion. The G-parity boundary condition is used and carefully tuned so that the ground state energy of the πœ‹πœ‹β‚β‚Œβ‚€ state matches the kaon mass. Three sets of πœ‹πœ‹ interpolating operators are used, including a scalar bilinear ``Οƒ" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fits and a bootstrap determination of the 𝑝-value have been used, and a detailed analysis of all major systematic error is performed. The πœ‹πœ‹ scattering phase shift results are presented in Fig. 5.10 and Tab. 5.12. For the Kaon decay amplitude, we finally get Re(𝐴₀) = 2.99(0.32)(0.59) Γ— 10⁻⁷GeV, which is consistent with the experimental value of Re(𝐴₀) = 3.3201(18) Γ— 10⁻⁷GeV, and Im(𝐴₀) = -6.98(0.62)(1.44) Γ— 10⁻¹¹GeV. Combined with our earlier lattice calculation of 𝐴₂ [2], we obtained Re(πœ–β€²/πœ–) = 21.7(2.6)(6.2)(5.0) Γ— 10⁻⁴, which agrees well with the experimental value of Re(πœ–β€²/πœ–) = 16.6(2.3) Γ— 10⁻⁴, and Re(𝐴₀)/Re(𝐴₂) = 19.9(2.3)(4.4), consistent with the experimental value of Re(𝐴₀)/Re(𝐴₂) = 22.45(6), known as the πœŸπ‘°=1/2 rule.


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More About This Work

Academic Units
Thesis Advisors
Christ, Norman H.
Ph.D., Columbia University
Published Here
November 3, 2021